CBSE Class 10 Maths (Standard) Sample Paper 2027 with Solutions: Download Official PDF & Marking Scheme

Particulars

Details

Board

Central Board of Secondary Education

Class

Class 10

Subject

Mathematics Standard

Subject Code

041

Academic Session

2026-27

Board Exam

2027

Sample Paper

Released

Maximum Marks

80

Exam Duration

3 hours

Total Questions

38

Marking Scheme

Released

SECTION – A (20 x 1 = 20)

This section comprises 18 multiple choice questions and two questions of assertion and reasoning type of 1 mark each.

Q. No

Question

Marks

1.

The greatest number which divides both 134 and 188, leaving remainders 4 and 6 respectively, is:

(A) 13 (B) 26 (C) 39 (D) 65 

2.

If f(x) = px ² + qx + r, p ≠ 0 and p + r = q, then one of the zeroes of f(x) is:

(A) q/p (B) r/p (C) −r/p (D) −q/p

1

3.

Tarun correctly solved a pair of linear equations in two variables and found their only point of intersection as (5, – 1). One of the lines was x – y = 6. Which of the following could have been the other line?

I: 3x – 3y = 18

II: 2x – 3y = 13

III: 2x – 3y = 16

(A) I only (B) II only (C) I and II (D) II and III

1

4.

If (1 – p) is a root of the quadratic equation x ² + px + 1 – p = 0, then its roots are:

(A) 0, 1 (B) – 1, 1 (C) 0, – 1 (D) – 1, 2

1

5.

The middle term of the A.P.: 10, 7, 4, …, – 62 is:

(A) – 26 (B) – 29 (C) – 32 (D) – 35

1

6.

The perimeters of two similar triangles are 56 cm and 70 cm respectively. If one side of the first triangle is 14 cm, then the corresponding side of the second triangle (in cm) is:

(A) 5 (B) 7.5 (C) 10 (D) 17.5

1

7.

The point which lies on the perpendicular bisector of the line segment joining the points A (– 3, – 4) and B (3, 4) is:

(A) (0, 0) (B) (0, 3) (C) (3, 0) (D) (0, 4)

1

8.

If tan (A + B) = √3 and tan (A – B) = 1/√3 , 0° < A + B < 90°, A > B, then the value of A and B respectively are:

(A) 60°, 30° (B) 60°, 45° (C) 45°, 15° (D) 60°,15°

1

9.

T-shirts marked with numbers 4 to 99 are placed in a box. Gunika is fond of numbers. She randomly takes out a T-shirt from this box. The probability that she gets a T-shirt marked with a number that is either a perfect square or a perfect cube is:

(A) 1/12 (B) 1/32 (C) 11/96 (D) 5/48

1

10.

The diameter of a car wheel is 21 cm. The number of complete revolutions it will make in moving 66 km is:

(A) 10 ⁴ (B) 10 ⁵ (C) 10 ⁶ (D) 10 ⁷

1

11.

Two cubes each of volume 64 cm3 are joined end to end to form a solid. The surface area of the resultant cuboid is:

(A) 192 cm ² (B) 160 cm ² (C) 96 cm ² (D) 80 cm ²

1

12.

The mean age of a combined group of men and women is 35 years. If the mean ages of the men and women are 38 years and 30 years respectively, then the percentage of women in the group is:

(A) 15 (B) 25.5 (C) 35 (D) 37.5

1

13.

Two dice are rolled simultaneously. The probability of getting number less than 4 on each die is:

(A) 1/4 (B) 1/9 (C) 1/36 (D) 1/6

1

14.

PM is a median of Δ PQR with vertices P (5, – 6), Q (6, 4) and R (0, 0). The length of PM is:

(A) 2√17 units (B) 2√15 units (C) √101 units (D) 10 units

1

15.

The arc of a circle is of length 6𝜋 cm and the sector it bound has an area of 24𝜋 cm ² . The radius of the circle is:

(A) 4 cm (B) 8 cm (C) 16 cm (D) 18 cm

1

16

The mean and median of the data are 35.5 and 32 respectively. The value of mode for this data is:

(A) 23 (B) 26 (C) 25 (D) 30 

1

17.

A flying kite is tied to a point on the ground with the help of a string. The string makes an angle θ with the ground level such that tan θ = 12/5 . If the length of the string is 52 m, then the height of the kite above the ground is:

(A) 40 m (B) 45.5 m (C) 48 m (D) 50 m

1

18.

2 cards of diamonds and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from this pack. The probability of getting a card of heart is:

(A) 13/52 (B) 13/46 (C) 11/52 (D) 11/46  

1

Assertion-Reason Based Questions Directions:

Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).

Select the correct answer from the options (A), (B), (C) and (D) as given below:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

19.

Assertion (A): If three vertices of a parallelogram taken in order are (–1, –6), (2, – 5) and (7, 2), then its fourth vertex is (4,1).

Reason (R): Diagonals of a parallelogram bisect each other.

1

20.

Assertion (A): If zeroes of the polynomial (2k – 1) x ² + 4x – 3 are reciprocal of each other, then k = –1.

Reason (R): If a = c, then zeroes of the polynomial ax ² + bx + c, a ≠ 0 are reciprocal of each other. 

1

CHECK: CBSE Class 10 Maths (Standard) Sample Paper 2026-27

Section

Question Numbers

Type of Questions

Marks

Section A

1–20

MCQs and Assertion-Reason

20

Section B

21–25

Very Short Answer

10

Section C

26–31

Short Answer

18

Section D

32–35

Long Answer

20

Section E

36–38

Case Study-Based

12

Total

1–38

—

80